Teaching

Algebra for coding theory and cryptography

I am currently giving a course on
Algebra for Coding Theory and cryptography,
aimed ad both undergraduate and graduate students.
The aim of this course is to introduce the
necessary mathematical tools for the construction of
encryption schemes and protocols and their cryptanalysis.
Among the topics presented there are:

Elements of group theory

Public-key protocols based on the discrete log problem:
Diffie-Hellman, ElGamal, STS and their variants

Pairing based cryptography: ID-based encryption and key escrow

Elements of number theory

RSA: implementation and cryptanalysis; OAEP and some security
models

Primality testing

Digital signature

Finite fields

The construction of AES

Cryptanalysis of a symmetric cryptosystem

Elements of the theory of Elliptic Curves

Random numbers and randomness

Cryptographic hash functions

Oblivious transfer and secure multipary computation

Homomorphic cryptography

Anonimity schemes

Error correcting codes

Network coding

More details and an extensive
bibliography are available (in italian) on
the following pages:

In 2013, I have been giving a similar course to the students of Civil
Engineering.

Combinatorial Geometry

I have also given a course on Combinatorial Geometry at
Università Cattolica in 2011. The aim of this course was to introduce
some of the most important techniques and results in Combinatorial
Geometry. In particular, among the topics discussed there will be:

Introduction to linear spaces and designs; the De Brujin-Erdős theorem
and some of its consequences

Parameters of a design and bounds
on the parameters of a symmetric 2-design

Hadamard 2-designs and Hadamard matrices: properties and some constructions;
extension of a design and Hadamard 3-designs

The Bruck-Ryser-Chowla theorem and its consequences

Finite projective spaces and finite projective planes

Arcs and ovals in a Finite projective plane: the theorem of Segre and
the existence of hyperovals in even characteristic

Topics in Algebra and Geometry

During the 2008/09 and 2009/10 academic years, I gave
a course on ``Topics in Algebra and Geometry'', offered
to 4th year students in Civil Engineering at
Università degli Studi di Brescia. Main topics of
this course are matrix theory and applications and an
introduction to curves and surfaces in projective spaces.
A bibliography and some lecture notes are available
here.

Algebra and Geometry

In the 2006/07 and 2007/08 academic years, I taught
course on Algebra and Geometry for first year undergraduate
students of Mechanical Engineering at Politecnico di Bari.
All relevant information is available (in italian)
here.